This invention relates to an improvement made to a scanning device that is capable of building a distortion-free two-dimensional image on a surface to be scanned, and more particularly to a scanning device configured to effect deflection and convergence of a light beam for the two scanning directions independently of each other.
Conventionally, there have been prior art systems to build an image by two-dimensionally scanning optical spots on a surface to be scanned, as disclosed in Japanese Patent Publication Sho44-9321 and Japanese Patent Provisional Publication Sho51-26050.
The two-dimensional deflection devices disclosed in these documents, however, have a problem when the angular position of on directional deflection is kept constant with respect to the other directional deflection, scanning on the surface to be scanned suffers from distortion, requiring a complicated and large-scale electrical system to electrically correct the light paths for scanning.
Japanese Patent Publication-Sho62-20524 and Sho62-20525 disclose arrangements to optically and mechanically eliminate such scanning distortion. Such scanning devices are, however, configured to deflect the light beam from a light source with a single deflector and therefore requires a complicated dual-axis drive mechanism for the deflector. The problem associated with the arrangement having no independent control mechanism for each scanning direction is described below with reference to FIGS. 1 through 3.
The example shown here employs a polygonal mirror for deflection and a so-called f.theta. lens with a distortion aberration with which the image height "h" should be equal to a product of the incident angle ".theta." by the focal length ".function.".
Accordingly, the image height "h" is given by EQU h=.function..multidot..theta.-(1)
In FIG. 1, numeral 10 indicates a rotationally symmetric (or spherical) f.theta. lens, whose optical axis coincides with the x-axis indicated by the dot-dash line.
Assuming a y-axis and a z-axis that are orthogonal to the x-axis and to each other, the y-z plane is supposed to be the surface to be scanned. Also assuming a point at which a light beam emitted from a light source not shown falls upon the reflection surface of the deflector as .largecircle..smallcircle., the light beam appears as if it is emitted from the point .largecircle..smallcircle. as shown in FIG. 1.
In a one-dimensional scanning device to deflect the optical spots formed on the surface to be scanned only in one direction on the y-axis or the z-axis, the constant velocity of the optical spot on the surface to be scanned is ensured by the effect of the aforementioned f.theta. lens, which makes the scanning lines linear.
If, in contrast, the optical spot is to be two-dimensionally scanned in the y-z plane, a problem is encountered as described below.
Assume that the intersection point at which the X-axis meets a virtual plane H (double-dot-dash line) perpendicular to the x- aixs is O.sub.1, while the intersection point at which it meets the scanning surface is O.sub.2, and further that the intersection point at which the incident light beam passed by point O.sub.0 to enter the f.theta. lens 10 at an angle of .theta.AX to the x-axis meets the virtual plane H is P.sub.1, while the intersection point at which it meets the surface to be scanned is P.sub.2. The angle between the light beam O.sub.0 P.sub.1 and the Z-X plane is then .theta..sub.y, the angle between the line segment made by reflection of the light beam O.sub.o P.sub.1 on the Z-X plane and the x-axis is .theta..sub.z, and the angle between the line segment O.sub.1 P.sub.1 and the Z-X plane is .gamma., as shown in an enlarged view of FIG. 2A. Further assume here that the intersection point at which the perpendicular line P.sub.1 to the Z-X plane meets the Z-X plane is P.sub.1, the equation holds: ##EQU1## therefore ##EQU2##
It also holds that where ##EQU3## and therefore ##EQU4## Thus, .theta.AX and .gamma. can be represented by the following equations: EQU .theta.AX=cos.sup.-1 (cos.theta.y.multidot.cos.theta.z) (2) EQU .gamma.=tan.sup.-1 (tan.theta.y/sin.theta.z) (3)
FIG. 2B illustrates the relationship shown in FIG. 2A, projected onto the individual planes for easier understanding of the above explanations. FIG. 2C shows a different way of representing the triangular relationship including Az for the same purpose.
As shown in FIG. 1, the angle between O.sub.2 P.sub.2 on the surface to be scanned and the z-axis is also .gamma., so O.sub.2 P.sub.2 is represented by the following equation as is understood from the equation (1), where the focal length of the f.theta. lens is .function.: EQU O.sub.2 P.sub.2 =.function..multidot..theta.AX (4)
Accordingly, the coordinates of P, P (y, z) are indicated by following equations EQU Y=.function..multidot..theta.AX.multidot.sin.gamma. (5) EQU Z=.function..multidot..theta.AX.multidot.cos.gamma. (6)
As is readily understood from the above equations (5) and (6), in such an optical system, the value y of the Y-coordinate and the value z of the Z-coordinate are both functions of .theta.AX, .gamma. so Y, Z are related to each other by way of .theta.AX, .gamma.. Consequently, when varying either .theta..sub.y or .theta..sub.z, while keeping the other constant, the displacement of the optical spot on the surface to be scanned is represented by the change in components in both Y and Z directions. In practice, curved scanning lines are produced as shown in FIG. 3. In order to minimize the curve so that the y-coordinate can be determined by .theta..sub.y, and the z-coordinate by .theta.z independently of each other, to thereby allow the line image to be linearly scanned, the scanning line indicated by the solid line in FIG. 3 must approximate the line indicated by the double-dot-dash line. For this purpose, the image building optical system should consist of an f.theta. characteristic plane satisfying an equation EQU O.sub.2 P.sub.2 =.function..multidot..theta.AX
and a correction surface with the F(.gamma.) characteristic in operative association with the f.theta. characteristic plane, the final y and z coordinates thereof being determined by EQU Y=Fy(.gamma.).multidot..theta.AX.multidot.sin.gamma.=.function..multidot..t heta.y EQU Z=Fz(.gamma.).multidot..theta.AX.multidot.cos.gamma.=.function..multidot..t heta.z
Fy(.gamma.), Fz(.gamma.): Correction function for varying the focal length by .gamma.
The above conditions can be generalized so that the image height O.sub.2 P.sub.2 is given by the above equation EQU O.sub.2 P.sub.2 =.function..multidot.g(.theta.AX)
For example, an f.theta. lens should satisfy EQU g(.theta.AX)=.theta.AX
If an arc sine lens is used, as with a galvanomirror, an equation shown below is satisfied ##EQU5##
.phi.=1 Amplitude of sine oscillation of galvanomirror
In this case, the image building optical system is required to provide the characteristics satisfying the relation: EQU Y=Fy(.gamma.).multidot.g(.theta.AX).multidot.sin.gamma.=.function..multidot .g(.theta.y) EQU Z=Fz(.gamma.).multidot.g(.theta.AX).multidot.cos.gamma.=.function..multidot .g(.theta.z)
The two-dimensional scanning device disclosed in Japanese Patent Publication Sho62-20520 compensates for the scanning distortion by mechanichallly rotating the scanning lens. This is an arrangement to two-dimensionally scan a single optical spot formed by a light beam from a point light source. Thus, it is still associated with such disadvantages as the upper speed limit for building a two-dimensional image and a complicated drive mechanism, because the deflector for deflecting light is driven through two axes, while also driving the scanning lens at the same time. Furthermore, there is another optical system proposed to simultaneously scan two optical spots by providing two light sources to thereby speed up the image building procedure. However, this cannot be a system of building an image by a single scanning process in terms of its principle as well as actual effects.